The Discrete Wiener-Hopf Equation Whose Kernel is a Probability Distribution with Positive Drift

The Discrete Wiener-Hopf Equation Whose Kernel is a Probability Distribution with Positive Drift Full article

Journal

Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260

Output data

Year: 2020, Volume: 61, Number: 2, Pages: 322-329 Pages count : 8 DOI: 10.1134/S0037446620020147

Tags

arithmetic distribution; asymptotic behavior; discrete Wiener-Hopf equation; inhomogeneous equation; positive drift

Authors

Sgibnev M.S. ¹

Affiliations

1	Sobolev Institute of Mathematics, Novosibirsk, Russian Federation

We consider the discrete Wiener-Hopf equation with inhomogeneous term g={gj}j=0∞∈l∞; the kernel of the equation is an arithmetic probability distribution generating a random walk drifting to +∞. We prove that the previously obtained formula for the Wiener-Hopf equation with general arithmetic kernel for g ∈ l1 is a solution to the equation for g ∈ l∞ and that successive approximations converge to the solution. The asymptotics of the solution is established in the following cases with account taken of their peculiarities: (1) g ∈ l1; (2) g ∈ l∞; (3) gj → const as j → ∞; (4) g ∉ l1 and gj ↓ 0 as j → ∞. © 2020, Pleiades Publishing, Ltd.

Sgibnev M.S.
The Discrete Wiener-Hopf Equation Whose Kernel is a Probability Distribution with Positive Drift
Siberian Mathematical Journal. 2020. V.61. N2. P.322-329. DOI: 10.1134/S0037446620020147 WOS Scopus OpenAlex

Web of science:	WOS:000540148100014
Scopus:	2-s2.0-85086338257
OpenAlex:	W3035135812

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